Here is one example of each:
Allusion--In the chapter titled "Rafaela Who Drinks Coconut and Papaya Juice on Tuesdays," Esperanza makes an allusion to Rapunzel. She says that Rafaela leans out the window and dreams that her hair is like Rapunzel's implying that Rafaela wishes she would be rescued from the metaphorical dungeon in which she lives with her husband.
Hyperbole--In the chapter titled "And Some More," the girls talk about the names that Eskimos have for snow. Nenny says that they have a million zillion names for snow to exaggerate the fact that no two snowflakes are alike.
Symbolism--In the chapter "Linoleum Roses," Sally pretends that she has the perfect life with her husband. He is controlling and abusive, and all day she dreams of the happy life she wishes she had. She stares at the rose pattern on the floor, a symbol of this desired life.
An interesting allusion is in the vignette entitled "The Family of Little Feet." In this section, Esperanza and her friends are trying on old high-heeled shoes. The girls feel as though it is Christmas because of the unexpected gifts. They also feel like Cinderella because they are wearing such fancy shoes. The allusions are presented as follows:
Today we are Cinderella because our feet fit exactly (40).
The First Annual Tarzan Jumping Contest
Immediately, the images of Cinderella and Christmas bring to mind the way the girls feel about their experience with the shoes. Furthermore, both Cinderella and Christmas are allusions a reader would probably know and identify.
Another allusion occurs in "Meme Ortiz" when some of the children in the neighborhood have "The First Annual Tarzan Jumping Contest." Since Tarzan is known for his ability to jump great distances between trees, this competition name is an allusion to his famed abilities.
Examples of hyperbole can be found in "Hips" and "Boys and Girls." When Esperanza discovers her figure is spreading with hips, she also realizes her little sister cannot relate to this new development. Esperanza uses hyperbole to describe the distance in understanding as follows:
Nenny, I say, but she doesn't hear me. She is too many light-years away. She is in a world we don't belong to anymore (52).
Nenny isn't really in a different world or light years away, but the hyperbole helps to explain the way Esperanza feels as she changes physically and mentally during puberty. Also, according to Esperanza, boys don't seem to understand girls, either. She explains the difference as follows:
The boys and the girls live in separate worlds. The boys in their universe and we in ours (8).
Living in a different world or universe from boys is physically impossible; therefore, the reference used here is an exaggeration. This exaggeration is used to explain how differently Esperanza views the lives of girls from boys.
As far as symbolism is concerned, the dominant symbol of the story is Esperanza's house. Esperanza is infatuated with the ideal home because it represents the perfect life she desires to lead. The house on Mango Street is not as luxurious as she would have it. Not only is it everything she doesn't want in life, but it also represents her feelings of inferiority and powerlessness due to poverty. Esperanza explains how she feels trapped and isolated with another symbol as seen in the following passage:
Until then I am a red balloon, a balloon tied to an anchor (9).
The color red symbolizes passion, which Esperanza has for life. The fact that she is also a balloon refers to the fact that she has a great desire to fly away. Unfortunately, this passionate flyer is tied to an anchor, a device that prohibits her from living a life she wants. The anchor could also represent poverty, her culture, or anything else that seems to keep Esperanza from escaping her circumstances.